Sound triangulation using cheap microphones

Sound triangulation is a method of determining where a sound originated from. Triangulation can give the location of a sound source in 2-d space. A sound wave travels out from its point of origin as a sphere. Trilateration is another method a locating the source of a sound. It is modeled around the fact that sound waves travel out spherically. See the below images for a better description of what I mean.

The equations for the Trilateration model of sound location were a bit difficult for me to understand well enough to build a project around them. Triangulation solves this problem by using a much simpler model of sound location. It assumes that all sound waves from a sound source travel out in a planer way(straight lines) instead of in a spherical way. This greatly simplifies the equation to a few variables that are related by basic trigonometry.

planer sound diagram

The equation is simplified to :

where: is the time difference in seconds is the distance between the microphones in meters is the angle between the baseline of the microphones and the incident sound, in degrees is the speed of sound